Combine 8 oz whole milk, 1 oz unsalted butter, 1 oz granulated sugar, 1 ½ teaspoons table salt and 1 large egg in a mixer bowl. Sprinkle 2 ¼ teaspoons dry yeast over the mixture. Mix on low speed to combine the ingredients.
Add 1 ½ (7½ oz) cups of the bread flour until the batter is very thick. If using a stand mixer, switch to the dough hook. With the mixer running, add the remaining flour (7½ oz). Knead the dough for 5 minutes until it is smooth and elastic. If mixing by hand add the flour using a wooden spoon and/or a plastic bowl scraper and knead on a floured surface.
Turn the dough out onto a lightly floured surface and knead into a smooth ball. Set in a lightly oiled bowl, turning once to coat the surface of the dough. Cover with plastic wrap and set aside to rise until doubled in volume (1 - 1½ hours).
Line two baking sheets with parchment paper or a silicone baking mat.
Turn the dough out onto a lightly floured surface. Divide the dough into 12 equal portions. Roll each portion to a tight ball. Starting with the first piece of dough you rolled, roll the dough to form a 6" long cigar shape. Set it on the baking sheet. Continue with the remaining dough, placing 6 rolls onto each baking sheet. Use the palm of your hand to flatten each roll to about 1/2" thick and 2" wide oval. If at any point the dough is too difficult to work with give it a 10 minute rest and then continue.
Cover the pans and set aside in a warm place to rise until almost doubled in height and it nicely puffed (about 1 hour). Meanwhile, preheat the oven to 400 °F.
Brush the tops of the buns with milk. Bake until the buns are golden brown and feel light when lifted off the sheet pan, about 10-13 minutes. Allow to cool completely before slicing.